Research Synthesis: The VIX as a Moderator of Small vs Large Cap Performance and the “Generals Lead the Troops”

Readers are encouraged to check out the following background reading:

On the VIX as a moderator of short-term relative performance between large and small caps: http://www.cxoadvisory.com/blog/external/blog7-12-06/

On the use of the S&P500 and Russell2000 relative strength relationship to predict S&P500 returns: http://marketsci.wordpress.com/2009/03/31/do-the-troops-lead-or-follow-the-generals/

Sometimes interesting findings results from combining two different ideas that are both good—sort of a chocolate and peanut butter kind of thing. In this case, the relationship between the S&P500 and the Russell2000 is interesting because it captures the lead/lag autocorrelation effect documented in the academic literature. In addition it also  captures the difference in risk premium to holding large diversified companies that are more heavily tied to economic factors versus smaller and more concentrated companies that have: 1) less sensitivity to economic factors most of the time, but more stock-specific risk 2) a high sensitivity under times of extreme stress–generally due to higher credit risk. Nonetheless, the explanantion and theory is a subject for another day (or another blog), my goal is to show that there is a synergistic effect by combining both. In the MarketSci post (see link above), a strategy was introduced that showed that the S&P500 tended to outperform when the 12-month or 1-year return was higher than the Russell2000 index. This phenomenon was labelled as the “Generals Leading the Troops.” This strategy did better   with less risk and less exposure than a standard buy and hold strategy. In the link above from CXO Advisory they review a paper by Dean Leistikow and Susana Yu who tested the significance of the relative VIX level as a signal for short-term switching between the Russell2000 (small-cap) and the S&P500 (large-cap) stock indexes. They found that the S&P500 outperformed the Russell2000 when the VIX was high, and underperformed when the VIX was low. These high/low levels were identified as being within 10-20% above or below the 75-day moving average of the VIX.

So with that background, lets get down to our little experiment to see how these two separate findings work together. In terms of methodology: I used the S&P500 and Russell2000 index prices from Yahoo Finance to increase the sample size of the dataset. I defined relative outperformance for the relative strength strategy as the 252 day return of the S&P500 being greater than(less than) the 252 day return of the Russell2000. For the VIX, I used the 75-day sma mentioned in the article, and decided to split the difference of 10-20% as being either 15% above or below the sma. Lets look at the results for each strategy in isolation, and in combination.

S&P500 Average Daily Performance Under Different Conditions (5000 bars)
(non-compounded–ie fixed bet)
		avg daily ret
	avg daily return	/avg daily sd	w% (next day)
Baseline (Buy and Hold the S&P500)	0.03%	0.17%	53.1%
S&P500 (SP) is leading Russell (RUT)	0.09%	0.71%	55.0%
Russell (RUT) is leading S&P500 (SP)	-0.01%	-0.10%	51.5%
VIX/75day sma>1.15  (Vsma75>1.15)	0.10%	0.88%	54.8%
VIX/75day sma<.85 (Vsma75<.85)	-0.02%	-0.28%	51.8%
SP> RUT  and (Vsma75>1.15)	0.22%	2.98%	58.0%
SP> RUT  and (Vsma75<.85)	0.10%	2.60%	54.60%
RUT> SP  and (Vsma75>1.15)	-0.01%	-0.16%	51.40%
RUT>SP  and (Vsma75<.85)	-0.11%	-2.10%	49.66%

Conclusions: The results for combining the two studies showed  higher absolute and risk-adjusted performance  than either study individually over most categories. It appears that the dual screen of relative strength and relative VIX are more powerful together than in isolation. On the positive side, when the S&P was leading the Russell and the VIX was high, the S&P had by far its best performance in absolute and risk-adjusted terms. On the opposite side, when the Russell was leading the S&P and the VIX was low, the S&P put in its worst performance in absolute and risk-adjusted terms. As a third note, the S&P performed well when the VIX was low and the S&P was outperforming the Russell. While not shown for brevity’s sake, it is clear that the S&P underperforms buy and hold in the “normal” VIX environment (1.15>VIX/sma>.85) regardless of whether it is leading or lagging. Creating long and long/short strategies based on these regimes is a subject for a future post.